I present a candidate for a new derivation of black hole
entropy. The key observation is that the action of General Relativity in
bounded regions has an imaginary part, arising from the boundary term. The
formula for this imaginary part is closely related to the Bekenstein-Hawking
entropy formula, and coincides with it for certain classes of regions. This
remains true in the presence of matter, and generalizes appropriately to
Lovelock gravity. The imaginary part of the action is a versatile notion,

I
will describe a discrete model of spacetime which is quantum-mechanical,
causal, and background free. The kinematics is described by networks whose
vertices are labelled with arrows. These networks can be evolved forwards (or
backwards) in time by using unitary replacement rules. The arrow structure
permits one to define dynamics without using an absolute time parameter.
Based on arXiv:1201.2489.

Causal
Dynamical Triangulations” (CDT) is a lattice theory where aspects of quantum
gravity can be studied. Two-dimensional CDT can be solved analytically and the
continuum (quantum) Hamiltonian obtained.

In this talk I will show that this continuum Hamiltonian is the one obtained by
quantizing two-dimensional projectable Horava-Lifshitz gravity.

We construct a
self-consistent model which describes a black hole from formation to
evaporation including the back reaction from the Hawking radiation. In the case
where a null shell collapses, at the beginning the evaporation occurs, but it
stops eventually, and a horizon and singularity appear. On the other hand, in
the generic collapse process of a continuously distributed null matter, the
black hole evaporates completely without forming a macroscopically large

Both AdS/CFT duality and more general reasoning from quantum gravity point to a rich collection of boundary observables that always evolve unitarily. The physical quantum gravity states described by these observables must be solutions of the spatial diffeomorphism and Wheeler-deWitt constraints, which implies that the state space does not factorize into a tensor product of localized degrees of freedom.

I will review some problems of the black hole paradigm and explore otherpossibilities for the final state of stellar collapse other than an evaporatingblack hole. In particular I will use the so-called transplanckian problem as aguide in this search for a compelling scenario for the evaporation ofultracompact objects.

I will recall the
main motivations for considering spin foam models in their Group Field Theory
(GFT) versions, which are quantum field theories defined on group manifolds. As
for any other quantum field theory, a fully consistent definition of the latter
must involve renormalization. I will briefly review a specific class of GFTs,
called tensorial, for which progress in this direction has recently been possible.
A new just-renormalizable model, in three dimensions and on the SU(2) group,

Tensor models are
generalization of matrix models, and are studied as discrete models for quantum gravity for more than two-dimensions. Among them, the rank-three tensor models can be interpreted as theories of dynamical fuzzy spaces, and they generally have the feature of

We describe of the evaporation
process as driven by the dynamical evolution of the quantum gravitational
degrees of freedom resident at the horizon, as identified by the Loop Quantum
Gravity kinematics. Using a parallel with the Brownian motion, we interpret the
first law of quantum dynamical horizon in terms of a fluctuation-dissipation
relation applied to this fundamental discrete structure. In this way, the
horizon evolution is described in terms of relaxation to an equilibrium state